This type of problem has been widely studied in the statistical and survey sampling literature. A commonly used approach is stratified sampling [1]}, [2]}, [3]},
where nodes (e.g., people) are partitioned into a set of non-overlapping categories (or strata). The objective is then to decide how many independent draws to take from each category, so as to minimize the uncertainty of the resulting measurement.
This effect can be achieved in expectation by a weighted independence sampler (WIS) with appropriately chosen sampling probabilities \(\pi ^{\scriptscriptstyle \textrm {WIS}}\) .
In our example, WIS samples Vatican residents with much higher probabilities than Chinese ones, and avoids completely the rest of the world, as illustrated in Fig. REF (b).
